Reduced Order Models of Low Mach Number Isothermal Flows in Microchannels

We present reduced order models of unsteady low Mach number isothermal ideal gas flows in two-dimensional rectangular microchannels subject to first order slip boundary conditions. The Navier-Stokes equations are simplified using Low Mach Number expansions of the pressure and velocity fields. This approximation allows decoupling the density from spatial pressure variations, thus simplifying the momentum equation. The resulting diffusion equation and the subsequent pressure-flow-rate relationship enables modeling the flow using analog circuit components. The accuracy of the proposed models is investigated for steady and unsteady flows in a two-dimensional channel for different values of Reynolds and Knudsen numbers.